When an acquisition-related approval requirement is established, there isn't always an associated requirement to track and report (on a summary basis) compliance with the requirement. Sometimes a National Defense Authorization Act will include reporting provisions relating to acquisition-related approvals if Congress think it's important enough to do so. Agency-level abuse or non-compliance with acquisition authorities are sometimes reported by GAO or an Inspector General and cause Congress to create a reporting provisions to deal with the non-compliance. Other times, federal agencies establish their own reporting provisions by including them in policy memoranda or FAR/Agency Supplements. So when you ask "who is tracking whether these have been approved and who is approving them," you can't always expect that a requirement to track and report the approvals necessarily exists. Two key parts of FAR Part 7 suggest there why there may be no government-wide reporting requirement. FAR 7.503(e) states (emphasis added):

Agency implementation shall include procedures requiring the agency head or designated requirements official to provide the contracting officer, concurrent with transmittal of the statement of work (or any modification thereof), a written determination that none of the functions to be performed are inherently governmental. This assessment should place emphasis on the degree to which conditions and facts restrict the discretionary authority, decision-making responsibility, or accountability of Government officials using contractor services or work products. Disagreements regarding the determination will be resolved in accordance with agency procedures before issuance of a solicitation.

FAR 7.503(b) states:

Agency decisions which determine whether a function is or is not an inherently governmental function may be reviewed...by appropriate Office of Management and Budget officials.

The word "may" suggests there might not be a strict reporting requirement based on law or regulation.

I cannot confirm with certainty whether or not there is a reporting requirement for your local activity, agency, or even government-wide. However, the response above may provide something that your "requirements team can grasp." If a contracting officer is concerned that a requirement for services which has been identified by the requiring activity may not be reasonably considered a "critical" requirement, the contracting officer should document the contract file accordingly and elevate the issue as needed. Of course, any such concerns should have been addressed during the acquisition planning stage.